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December 1996/January 1997 | Volume 54 | Number 4
Teaching for Authentic Student Performance Pages 26-29

Carol S. Parke and Suzanne Lane

How can teachers become better informed about performance assessment? How can the information that performance assessment tasks provide help teachers to strengthen their curriculum and improve their teaching techniques? How can teachers help their students understand why these tasks are important and how tasks are scored?

Information gathered from the use of performance assessments in one reform oriented mathematics education project can help to answer these questions. Since the 1990 1991 school year to the present, six schools have participated in the QUASAR Project. The goal of this project is to demonstrate how math programs that focus on problem solving and reasoning skills can succeed with urban middle school students of various ethnic backgrounds (Silver and Stein 1996).

For this project, we developed the QUASAR Cognitive Assessment Instrument (QCAI) and used it to monitor student outcomes and growth (Lane 1993). This instrument consists of a set of open ended tasks that measure students' mathematical problem solving, reasoning, and communication skills. We used a holistic rubric to score student responses to each task on a scale of 0 to 4, and we conducted in depth analyses of student performance. Over the years, the QUASAR teachers participated in various activities that helped them use this information about their students' mathematical understanding.

Learning About Performance Assessments

For performance assessments to have a positive impact on instructional practices in the classroom, teachers need to become familiar with the nature of the tasks, what content and thinking skills the tasks assess, and what constitutes a high quality response. Teachers in the QUASAR schools participated in workshops and collaborated informally with their colleagues to gain these types of experiences. They focused on two important aspects of performance assessment:

Performance assessments allow students to show how they arrived at their solutions and providing explanations for their answers, thereby providing rich information about students' thinking and reasoning.

Performance assessments reveal different levels of understanding of the mathematics content. Therefore, evaluations of student responses should focus on the content of the response, not its length.

Providing Answers and Explanations

At one school, teachers worked with their resource partner a mathematics educator at a nearby university to discuss the in depth analyses of student responses to a specific task. The task required students to choose the decimal number with the largest value from a list and to provide an explanation for their answer.

Many students in this school received low scores: Although they could select the correct answer, they were unable to successfully explain how they arrived at that answer. One teacher could not understand why it was necessary for students to provide an explanation. She reasoned that "the answer is the most important part; if they've got it right, there's no need to look at the explanation."

To illustrate the importance of an explanation, the resource partner showed teachers several examples where students had chosen the correct answer but did not necessarily understand why (see Figure 1).

Figure 1. The Importance of an Explanation

The first response displays complete and correct knowledge of decimal place value and illustrates why .8 has the greatest value. The second response includes a very incomplete and vague explanation that provides no indication of whether the student has any understanding of decimals. The third response demonstrates a misunderstanding of the value and placement of zeros in a decimal.

When the teachers compared the explanations, they began to see how much insight those explanations can provide into a student's level of understanding. This discussion was one of the first meaningful interactions these teachers had about their students' conceptual understandings and what they were learning in the classroom.

Looking for Content-Rich Explanations

A team of teachers at another school examined their students' responses to the QCAI tasks and agreed that they needed to place greater emphasis on written communication skills. Several students wrote lengthy explanations for some of the tasks, but those explanations contained few to no references to the mathematics in the task.

For example, one problem asked students to pretend to be radio announcers describing a race. First they had to read a graph that charted the times and distances run by the two racers. The task was designed to assess student performance in interpreting and integrating the two dimensions time and distance of a graph in a meaningful way.

One student wrote an elaborate description, but it did not incorporate the mathematical aspects of the graph. This student interpreted the line graphs as if they were simply the "paths" of the two runners. It appears that the student got so caught up in being a radio announcer that he overlooked the time and distance values on the axes of the graph. One teacher noted, "So it's not that they don't write, it's what they write." She then suggested that the teachers in her school should collaborate to identify ways to get students to write higher quality mathematical explanations.

Using Results to Inform Instruction

As the above examples illustrate, QUASAR teachers were becoming better informed about the nature of performance assessment tasks and the ways in which students respond to them. In other situations, groups of teachers used QCAI results to identify curriculum strengths and weaknesses. By examining the percentage of students at each score level for each task, teachers were able to evaluate the impact of their instructional program.

On one occasion, for example, 49 percent of the students received a high score (3 or 4) on a visual pattern task in the fall, while that number dropped to 16 percent in the spring. The teachers reasoned that the decrease occurred because while their instruction focused heavily on visual patterning just before the fall administration, they had provided no instruction on this topic during the remainder of the year. As a result of this discussion, the teachers modified their curriculum to ensure that they revisited this important area throughout the year.

In another instance, an after school workshop for teachers focused on the importance of patterns and functions throughout the middle school mathematics curriculum. The QCAI task required students to draw the next figure in the pattern and then describe the pattern. On examination, teachers saw that while the students seemed reasonably successful in drawing the next figure correctly, they had a great deal of difficulty describing the pattern.

The teachers began to see the importance of giving students frequent opportunities to explore and discover patterns and then gradually providing opportunities for them to describe, extend, and generalize a wider variety of patterns and functions using tables, graphs, and symbolic equations. These activities helped teachers modify and enhance their curriculum and instruction.

Familiarizing Students with the Assessments

To ensure that all students have the opportunity to perform their best, it is important that students become familiar with the open ended nature of assessment tasks, the type of content and thinking skills such tasks assess, and the criteria used to evaluate their responses. Teachers in the QUASAR schools frequently used the QCAI practice tasks to achieve these goals.

One way that teachers used the task materials was to illustrate that multiple strategies can be used to solve a problem. For example, student solutions to the task in Figure 2 show three possible strategies for obtaining a correct solution. The first student used common multiples; the next student drew three separate diagrams of blocks; and the third student performed three separate long divisions and showed that they all resulted in a remainder of 1. When students shared their strategies and responses, they gained a deeper conceptual understanding of the content and began to see there is more than one way to solve a problem.

Figure 2. Multiple Responses

Teachers also engaged students in activities designed to ensure that they understood the scoring criteria used to evaluate their work. A two day activity in one teacher's classroom resulted in a very successful learning experience for everyone involved.

First, students worked in small groups to solve a set of tasks located at different stations throughout the room. After each group had worked through the tasks, the teacher explained the criteria for each score level. Then, as a class, students examined a set of sample student responses that had been scored using these criteria.

On the following day, the students exchanged papers and scored one another's responses. The teacher discussed the importance of being objective and consistent when evaluating student work. This discussion helped students take the activity more seriously, and also to think hard about what constitutes good mathematical thinking. The students recorded the score they assigned, wrote a rationale for that score, and suggested ways to improve the response.

Figure 3 shows a response to a QCAI task that involves interpreting a graph of the speed of a boy going to his grandmother's house. The group of students who evaluated this response assigned it a score of 2 on a scale of 0 to 4. As a rationale for assigning that score, the students pointed out where the response was incorrect. For example, the story says Tony stopped his walk from 1:30 to 2, neglecting to note that the graph records his speed at this time. And they noted that the response was somewhat incomplete, because the story did not mention Tony's increase in speed before arriving at his grandmother's house. The figure also shows the students' suggestion for improving the response. Teachers found that instructional activities not only prepared students to take the QCAI, but promoted their engagement in challenging mathematical tasks and in discussions about what constitutes a good mathematical response.

Figure 3. Interpreting a Graph

Benefits for Teachers and Students

Professional development experiences and collaboration with colleagues can help teachers in all subject areas become better informed about the nature of performance assessment tasks. These experiences also can provide teachers with the insights they need to strengthen curriculum and improve instructional techniques.

In addition, teachers can use various challenging and engaging activities to introduce students to performance assessment tasks and to familiarize them with the criteria used to evaluate their responses. As a result, students develop a better understanding of what constitutes high level thinking and reasoning.

References

Cai, J., Magone, M. E., Wang, N., and Lane, S. (1996), "A Cognitive Analysis of QUASAR's Mathematics Performance Assessment Tasks and Their Sensitivity to Measuring Changes in Middle School Students' Thinking and Reasoning." Research in Middle Level Education.

Lane, S. (1993). "The Conceptual Framework for the Development of a Mathematics Performance Assessment." Educational Measurement: Issues and Practice 12, 2: 16 23.

Lane, S., and C. S. Parke. (April 1996). "Consequences of a Mathematics Performance Assessment and the Relationship Between the Consequences and Student Learning." Paper presented at the annual meeting of the National Council on Measurement in Education, New York.

Magone, M. E., J. Cai, E. A. Silver, and N. Wang. (1994). "Validating the Cognitive Complexity and Content Quality of a Mathematics Performance Assessment." International Journal of Educational Research 21, 3: 317 340.

Parke, C. S., S. Lane, and F. Guo. (April 1995). "The Consequences of a Performance Assessment in the Context of a Mathematics Instruction Reform Project." Paper presented at the annual meeting of the National Council of Measurement in Education, San Francisco.

Silver, E. A., and M. K. Stein. (1996). "The QUASAR Project: The Revolution of the Possible' in Mathematics Instructional Reform in Urban Middle Schools." Urban Education 30, 4: 476 522.

Endnotes

We draw on studies (Parke, Lane, and Guo 1995; Lane and Parke 1996) that collected data from teachers, resource partners, and administrators regarding the consequences of a mathematics performance assessment (QCAI).

See Magone and colleagues (1994) and Cai and colleagues (1996) for a further discussion of the analysis of student responses to the tasks.

To monitor student progress and the instructional program, the QCAI was administered in the fall and spring of each year. The task materials included actual tasks used in earlier years.

The QUASAR Project, is a University of Pittsburgh project funded by the Ford Foundation and directed by Edward A. Silver at the University of Pittsburgh.

Carol S. Parke is a Research Specialist in the School of Education, University of Pittsburgh, SCOI Forbes Quad, University of Pittsburgh, Pittsburgh, PA 15260. (e mail: csparke@vms.cis.pitt.edu). Suzanne Lane is a Associate Professor of Research Methodology, in the School of Education, University of Pittsburgh, SCOI Forbes Quad, University of Pittsburgh, Pittsburgh, PA 15260 (e mail sl@vms.cis.pitt.edu).

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Learning from Performance Assessments in Math

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December 1996/January 1997 | Volume 54 | Number 4 Teaching for Authentic Student Performance Pages 26-29 Carol S. Parke and Suzanne Lane How can teachers become better informed about performance assessment? How can the information that performance assessment tasks provide help teachers to strengthen their curriculum and improve their teaching techniques?

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Reworking the Workshop for Math and Science - Educational Leadership

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October 2003 | Volume 61 | Number 2
Teaching All Students Pages 6-11

Carol Ann Tomlinson

Several years ago, I was talking with a colleague who was teaching in a center-based school for students whose IQ scores registered above 140. She thought deeply about how to stretch her students, whose ceilings of possibility often go unexplored in heterogeneous classrooms. She was a good teacher in that setting. She knew it. Her students knew it. Their parents knew it. So I was surprised by what she said that day.

"I want to go back to a general education classroom next year," she began.

I want to see what would happen if I tried teaching this curriculum to a varied group of students. I believe I could make it work, and it's important to me to know whether I can.

She got her wish. Her new group of 5th graders in a different school the following year was certainly diverse. She had students with identified special education needs, students who could not yet read in any meaningful way, students who were learning to speak English, students who were working at grade level, and students who were more capable than many in her previous school. She taught them-all of them-the high-challenge curriculum that she had been using with her class of very advanced learners.

To say that no problems emerged and that everyone rose fairy-tale-like to the challenge would be satisfying. But it would not be honest.

The truth is that my friend had to make many adaptations in her new classroom that were not necessary in her former setting. She had to find time to work intensively with students who were not yet literate to ensure their growth in the gatekeeper skills of reading and writing. She had to find ways to support some students whose caregivers could not provide transportation, Internet access, or project materials. She had to teach inquiry skills to many students who had not previously encountered them. She even had to figure out new ways to extend the advanced curriculum for students whose reach already exceeded its parameters when the year began.

In many ways, this veteran teacher felt like a novice. She wasn't always sure how to arrange time to work with small groups of students with particular needs. She often wasn't certain how to express abstract ideas so that the concrete thinkers could confidently approach them. But from the beginning of the year, one fact was clear: Her classroom was a magnet for each student who spent 5th grade with her.

Discovery was a given. Doing was a way of life. Students learned to do better than what they perceived to be their best. Skills had an identifiable purpose. School was the place to be. Learning was the thing to do. No one wanted the year to end.

We could say that this teacher decided to "differentiate instruction in a mixed-ability classroom"-that she decided to "teach them all" in a heterogeneous setting. It would be tempting to say that she was a poster teacher for differentiation of instruction.

But I learned something more important from her and her students. As I watched their journey, I realized that she was asking a set of questions about teaching different from those we often ask-a profoundly important set of questions.

Framing the Questions

My colleague had already posed the most fundamental of the questions related to academically diverse populations: Do I intend to teach each individual child?

Although there seems to be only one answer to the question, the reality is more complex. The circumstances of teaching make it far more likely that we respond by saying, "I intend to teach the curriculum in as reasonable a way as I know how, and I hope that most of the students will respond."

My friend's answer signaled her willingness to accept responsibility for the success of each individual, regardless of the circumstances of that student's life.

To teach each student from his or her point of entry into the curriculum and perspective as a learner is more than difficult. It is a goal beyond the grasp of even the most expert teacher. The outcome for students who are outliers, however, is likely to be vastly different when a teacher pursues that elusive goal than when the teacher-by intent or default-abandons it. This particular 5th grade teacher elected to teach in pursuit of that goal, and her commitment made a world of difference in her classroom.

My colleague asked other questions about her academically diverse learners and how she would respond to them. The way she framed her questions was different from what I suspect is customary, and the subtle differences yielded powerful distinctions in her work.

This teacher did not ask, What labels do my students have? Rather, she asked, What are their particular interests and needs? Because needs rather than labels guided her instruction, students moved freely among peers and opportunities. Both her teaching and her students seemed less restricted, freer.

She did not ask, What are my students' deficits? Instead, she asked, What are their strengths? Although she clearly understood the need to "patch holes" in the fabric of their proficiency, beginning with what students could do changed the tone of the classroom and the will of reluctant learners.

In place of asking, How do I remediate students?, she pondered, What can I do to ensure that each student works at the highest level of thought and production possible? She understood that purpose propels human beings and that rich, purposeful curriculum propels students to master whatever skills they need to succeed.

This teacher did not ask, How can I motivate these students? Instead, she wondered, What releases the motivation born in all humans?

She did not ask, What do I do if a student cannot accomplish my agenda? She asked, How might I adapt the agenda to work for the student?

I also came to understand the subtle but crucial distinction in one other common school question. My friend did not ask, Where should we put this student? Instead, she asked, What circumstances will be the most effective catalyst for this student's development?

Taken singly, the questions are interesting and fruitful. Taken as a group, they are transformational. They are questions in search of equity and excellence for each learner.

Seeking Equity and Excellence

The United States has always balanced precariously on the twin values of equity and excellence. As a people, we believe that birth in a log cabin should not be a barrier to the boardroom or the Oval Office and that all citizens should have access to the opportunities that will help them realize their potential.

Similarly, we cling to a vision of the United States as representing the best. We stand for the fastest cars, the tallest buildings, the finest medical care, and the most innovative technology. We are committed to excellence. Let the world generate a problem: We will solve it.

To lose either equity or excellence as a guiding value would be to lose our identity. To maintain both, however, is a balancing act of the highest order. And the challenge is perhaps greatest in the schools that shape young people to be good stewards of these values. Although we don't often think about the impact of education decisions on the balance between equity and excellence, many decisions push the fulcrum in one direction or the other-for individual learners, groups, or schools as a whole.

A curriculum furthers excellence when it opens doors to a promising tomorrow. Instruction furthers excellence when it moves a learner as effectively as possible toward expertise as a thinker, problem solver, and producer. And procedures, policies, and practices further equity when they maximize the likelihood that each learner will be a full participant in an excellence-based education.

The 5th grade teacher's questions were her guideposts to achieving equity and excellence for the widest possible range of students. Her decision to move from a school where a complex, dynamic curriculum was a given to a classroom where that was less likely was an excellence-based decision. She wanted to ensure that a maximum number of students see themselves as worthy of wrestling with ideas and issues, just as adults do.

Had she made any other assumption in her mixed-ability classroom, her most able students would have experienced "excellence" devoid of challenge and sweat. For such students, this sort of pseudo-excellence is at first seductive but ultimately crippling. She refused to be a thief of challenge for her most advanced learners. Beginning with high-quality curriculum and instruction is a precursor to excellence for any student. For this teacher, labels did not define access to quality of thought or production. Rather, quality was the foundation from which learning for all students could emanate.

Equity in this teacher's classroom was also central. Her pivotal, equity-based decision was determining that a wide range of learners should have access to excellence. Then she immediately began asking herself, How do I support each student's persistent movement toward excellence and expertise? Equity not only grants access but also supports success. A plan to teach students skills that they had missed in the past was in operation, but never as an end in itself. Such "remediation" was always in the service of "acceleration."

Grappling with the Messiness of Teaching

Uncertainty is inherent in teaching. Although we can seldom guarantee the results of our decisions, we must make decisions, nonetheless. In a time when we find our student populations becoming exponentially more diverse, we still find ourselves asking such questions as, What is the right label for this child? Is the general classroom best or is a resource setting preferable? Can differentiation meet the specialized learning needs of students? Should specialists focus their energies on students or teachers?

The reality is that these questions lead us nowhere. Labels often stigmatize without offering a counterbalancing benefit. Some general classrooms cripple students, and other general classrooms are almost holy in their capacity to evoke the best in a wide range of learners. Likewise, some resource rooms become prison-like in limiting options for students who become dependent on them, whereas other resource rooms open access to a better future.

Differentiation can reinforce status, or differentiation can liberate students from stereotypical expectations. One specialist can touch hundreds of lives through successful collaboration with a single teacher, whereas other specialists are wasting their time attempting collaboration. Students, even of a given "category," differ greatly. The contexts in which we might provide services for them defy generalization.

If we reframe the questions that we ask, a tectonic shift might occur in how we make decisions on behalf of academically diverse learners. Not, What labels? but, What interests and needs? Not, What deficits? but, What strengths? Not, How do we remediate? (or even How do we enrich the standard curriculum?) but, How do we maximize access to the richest possible curriculum and instruction? Not, How do we motivate? but, What would it take to tap the motivation already within this learner? Not, Which kind of setting? but, What circumstances maximize the student's full possibilities?

Ultimately, just one question might best serve diverse learners, their teachers, and their society. What can we do to support educators in developing the skill and the will to teach for each learner's equity of access to excellence?

Carol Ann Tomlinson is Professor of Educational Leadership, Foundations, and Policy Studies, Curry School of Education, University of Virginia, P.O. Box 400277, Charlottesville, VA 22904; cat3y@virginia.edu.

KEYWORDS

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October 2003 | Volume 61 | Number 2 Teaching All Students Pages 6-11 Carol Ann Tomlinson Several years ago, I was talking with a colleague who was teaching in a center-based school for students whose IQ scores registered above 140.

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ERIC - The Mathematics Workshop Model: An Interview with Uri Treisman., Journal of Developmental Education, 1993

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Uri Treisman describes the development of his model to help minority students succeed and progress in mathematics, emphasizing group work and integrated instruction and student services. Explains his influences, core ideas informing the workshop model, structural impediments to success in the curriculum, existing programs, and other related topics. (DMM)

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Sign in to The Daily CAFE - The Daily Cafe

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The Daily CAFE is a Professional Development website designed for teachers and literacy coaches using The Daily 5 and The Literacy CAFE Assessment System. It is loaded with professional video and downloads, all created for teachers like you!

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Teacher to Teacher Ideas in the Top Teaching Blog | Scholastic

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Exciting lesson ideas, classroom strategies, teaching tips, book lists, videos, and reproducibles in a daily blog by teachers from the classrooms of extraordinary mentor

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Explore Houghton Mifflin Harcourt's curriculum. Browse our personalized K-12 classroom solutions by subject and program to discover ways HMH can...

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Effective Small Group Differentiated Instruction

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Classroom Management Strategies To Take Control Of Noisy Students

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Managing a Math Workshop by Clutter-Free Classroom

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These materials are available at http://www.teacherspayteachers.com/Product/MATH-WORKSHOP-ROTATION-BOARD An overview of the math workshop rotation board created by Clutter-Free Classroom {CFClassroom.com} This is the math workshop rotation board I use in my classroom. I designed the stations to spell out MATH MATH FACTS AT YOUR SEAT TEACHER'S CHOICE HANDS-ON MANIPULATIVES Included in the kit are the rotation cards, title, group numbers and pocket job titles.

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Math Workshop Model: Teaching Elementary Math

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Math Workshop Model: Teaching Elementary Math

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What is math workshop?

When many people, even teachers, hear the word math, their stomachs start to tighten up. They think that math is hard, not easily understood and too complex to really get. It doesn't have to be that way. Math is the science of numbers and patterns. Since math is an integral part of our lives, it is critical that people understand how math works.

So what is math workshop and how can it help young people to not only have a greater understanding of math, but to love math? Math workshop is a method of delivering math instruction. Many teachers are familiar with Reader's Workshop or Writer's Workshop. Math workshop is very similar in its approach. Not only is math workshop productive, it saves you time as a teacher. With new national mandates for special education and the Response to Intervention (RTI) requirements, math workshop will help you to achieve these intervention strategies easily and effectively not only for your special education students, but for all students. There is great talk in the education world about differentiated instruction. Math workshop is a model of instruction that brings differentiation to new levels.

What do I need to start math workshop?

To initially start, the only things that you need are a positive attitude, a willingness to try something new, and questions. I will tell you that I have moved into this method of instruction slowly. I started out last year with just asking students "what do you notice?" and recording their results. By starting out with this, I was able to build my confidence in both my understanding of math workshop as well as the belief that my students really could do this. As I saw the growth in my students and the knowledge that they already possessed, I knew that I was ready to move forward with this style of instruction. As a teacher, you will be amazed at the confidence that your students will gain as well as the depth of learning that will unfold before your eyes.

As you begin to feel comfortable in your math workshop skills, take on one portion at a time. It is ok and actually highly recommended that you move into this slowly. As you gain confidence you can add more parts to it.

What are the components of math workshop?

There are three major components of math workshop. They are the mini lesson, the work stations, and the reflection.

1. Math Workshop Launch

The launch starts out with an introduction to your objective for the day. It is not the time in which you will conduct most of your teaching. This is the time where students begin to think about what they already know about this topic. This is in essence the idea of activating their prior knowledge. I usually begin my launch with a question that prompts students to think about what they already know.

Questioning is a key part to the development and structure of math workshop. As you ask students open ended questions, it builds their observation skills, activates prior knowledge, and allows students to make connections. This is about 5-15 minutes in length. It is an introduction only. For great questioning techniques, I use Betty Garner's book Getting to Got It. It is a wealth of information.

2. Math Workshop Stations or Centers

Work stations, learning groups, centers. These are all different names for the same thing, cooperative learning groups. In the math workshop model, students spend the majority of time working together to process their thinking and learn from one another. This is the bulk of the learning time. Each station is about 12 minutes in length with a few minutes in between for transitions.

Work stations can be created in many different ways and are composed of many different things. Here are some examples of ways that work stations are used in math workshop classrooms.

Computer stations. Computer games are a way in which a variety of math skills are reviewed and reinforced.

Math games. These activities allow students to have fun while practicing a new skill or one that needs additional practice.

Teacher led instruction. This station is one in which the teacher guides student learning in the new skill for that day.

Building models. Constructing models of math problems using a variety of manipulates is a great way to exercise a student's brain and expand his or her thinking.

Writing. Writing in math allows for a two fold skill. Students are not only building writing fluency, but they are expressing their understanding in words. The teacher is then able to clearly see what the student knows.

Ongoing projects. Long term projects are also great ideas to use in work stations. They can keep students exploring more deeply about a particular idea.

The focus in this part of math workshop is to keep students active, engaged, and learning throughout this time. The more hands on the stations are, the more involved students will be and the deeper the learning that will ensue.

3. Math Workshop Reflection

The reflection piece is not only important, it is probably the most important part of workshop. Why? This is the place where students share their learning and the teacher gathers data. No, not formally gather data, but information about what students really learned and what students are still confused about and need some further instruction on. This portion should run about twenty minutes in length. It is longer than the mini lesson but much shorter than the activity part.

So why is it so important to gather this data? This is where your planning begins. By learning and taking careful note of what students really got and what they still need to learn, you are able to make some very specific, concrete decisions about what will be taught in the next few days. Perhaps you found that some students are still having trouble with addition with carrying. You can then set up a work station that reviews and reinforces that learning concept. In addition to that you can also make some decisions about possibly working with a small group of these students to give these kids more practice in this area of math.

Math Workshop in the Early Grades

I have just this summer read this amazing book, Math Exchanges, by Kassia Omohundro Wedekind. It has really changed some of my thinking on how to approach math workshop in the early years. As I move my teaching assignment from fourth grade to first grade this coming school year, I will be adding some ideas think about for grades K-2. In the meantime, I highly recommend reading this book. (Updated August 2012)

How do I incorporate math workshop into my classroom?

Grouping Students

There are some decisions that need to be made when putting groups together. Certainly personalities need to be considered. We all know that not every student will get along with each person in the class. There is no right or wrong way in grouping your kids. I feel that mixing the abilities in groups is more advantageous to everyone. By mixing ability levels, students can work together to gain a better and clearer understanding of a concept. As time goes on, lower ability students gain more confidence and a stronger voice from working in these groups.

The number of students in each group will vary based on your classroom size and time alotment for math. My math block is about an hour and a half. The first five to ten minutes is the mini lesson and the work stations consist of about an hour. I have four groups and each group rotates to a different work station about every twelve minutes. Three of the stations are student led and one is teacher led. During the teacher led station, I give my instruction for the day. With my thirty students, it leaves about seven or eight students in my groups. This is not ideal in my opinion. I would prefer to have about five in each group but due to time constraints and class size, it is what I have to work with.
Materials and Resources
The easiest thing to incorporate is a math notebook. In my students' notebooks, I have them answer questions, keep track of their own thinking, reflect on ideas and ask questions about things that they are still wondering about. All students are required to keep a notebook and I check it often.

Games and activities can be found in many places. If your math series has games that your students play, this is a great place to add those in. Some commercially generated games work well also. Online computer games are an easy resource to use and your imagination as well. The more creative you are with your ideas, the more excited students will be in their engagement in the lesson and activities.

How will math workshop benefit my students?

In my journey through moving my instruction to a math workshop model, my students never ceased to amaze me. After the first chapter test, I saw my students test scores result in higher grades than I had ever seen in my years of teaching in my school district. I also saw an excitement in doing math that was new in my students. Gone were the looks of apathy and groans as they took out their math materials. They were replaced with enthusiastic smiles and quick steps to our carpet for our mini lesson.

How does math workshop benefit me as the teacher?

I will tell you that I have moved into this method of instruction slowly. I started out last year with just asking students "what do you notice?" and recording their observations. By starting out with this, I was able to build my confidence in both my understanding of math workshop as well as the belief that my students really could do this. As I saw the growth in my students and the knowledge that they already possessed, I knew that I was ready to move forward with this style of instruction. As a teacher, you will be amazed at the confidence that your students will gain as well as the depth of learning that will unfold before your eyes.

As I stated before, it also allows an easy opportunity to differentiate learning for your students. You can adjust activities to scaffold the learning needs of struggling students while bumping up the challenges for students who are more advanced. This fits perfectly in with the RTI tiers that are now mandated across the nation. By moving to the workshop model, you are already building in those interventions that are required in this process.

Math is Fun! A Lesson in Letting Go

I think that teachers are by nature control freaks (myself included). They want to be sure that learning is taking place and the only way that can happen is by delivering all of the information as a lecture style format. I can attest that this is not the best way to have your students learn. Do you like to sit all day and listen to someone lecture? I don't know about you but I have sat in many teacher trainings and doodled, written notes to the person next to me, and written my grocery or to do lists. Aren't kids the same way? We observe the glazed over looks on their faces and wonder, why aren't they getting this? Why do I have to continue to reteach this? Dear very smart teacher, they are BORED!!!! So what do you need to do as the teacher? Let go. It is hard, I know and I still struggle with it. Believe in your students. They know so much more than you think that they do. As you and your students become more comfortable with the questioning process and workshop model, your students will begin to question each other and they will deepen their learning.

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Math Workshop Model: Teaching Elementary Mathematics

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When many people, even teachers, hear the word math, their stomachs start to tighten up. They think that math is hard, not easily understood and too complex to really get. It doesn't have to be that way. Math is the science of numbers and patterns.